Precoding has been used as a breamforming technique by weighing a signal stream with an appropriate phase and gain in order to optimize signal transmission at the receiving end. In the advent of the multi-user-multi-input multi-output (MU-MIMO) technology, multiple users could be served by the same radio resource. This could be accomplished by weighing the signal stream of a user or a user group with a precoding vector that is orthogonal from the precoding vectors of other users or user groups.
FIG. 1A illustrates a typical transmitter which operates using a precoding matrix. A type transmitter may have a processor 101 which may have a precoding unit 107 inherent to the processor 101. The processor 101 could be electrically connected to a storage medium 104 such as a disk drive or a flash drive. The storage medium 104 may have a predefined codebook 106 native to the storage medium. The processor 101 would be electrically connected to an analog to digital (A/D) converter and/or a digital to analog (D/A) converter circuit 102 which would be connected to a transceiver circuit 103. The transceiver circuit 103 would be connected to one or more physical antennas 105_1, 105_2 . . . 105—n. 
Conventionally, the precoding matrix could be constructed based on a channel state information (CSI) extracted from a user feedback such as a preferred precoder index of a predefined codebook. Assuming that the transmitter is the transmitter of a base station, upon receiving a user feedback, the base station may select an appropriate precoding matrix that corresponds to the user. The selected precoding matrix could be according to the user feedback or independent from the user feedback. After selecting the precoding matrix, the precoding unit 107 or the processor 101 would weigh the signal stream of a user according to the selected precoding matrix. The modified signal stream would then be transformed by the D/A converter circuit 102 into an analog signal which would be up-converted by the transceiver circuit 103. The signal stream would then be transmitted by the transceiver circuit 103 through one or more antennas 105_1, 105_2 . . . 105—n along with other signal streams simultaneously.
FIG. 1B illustrates an example of a codebook in accordance with a current version of the Long Term Evolution (LTE) standard. The codebook contains 16 PMIs numbered from 0 to 15, and precoder tables for each number of layers.
In cases in which the complete channel knowledge is available at the transmitter, two of the most common linear precoding techniques to construct a precoding matrix may include Conjugate Beamforming and Zero-forcing Beamforming. Assuming that H denote a N×L channel matrix between N antenna ports and L concurrent UEs. By using the Conjugate Breamforming technique, a precoding matrix, W, would be constructed as W=cH*, where H* is the complex conjugate of H. In other words, Conjugate Beamforming may simply take the complex conjugate of each channel coefficient in H as the breamforming weight, normalized by c. By using the Zero-forcing Breamforming technique, a precoding matrix, W, would be constructed as W=cH*(HTH*)−1. The Zero-forcing Breamforming technique would employ the CSI to precode the data-bearing symbols so that they sum to zero, or a ‘null’, at unintended receivers. For these linear precoding techniques, each column of W would serve as the precoding vector of data intended for a specific UE or a specific UE group.
Both of these linear precoding techniques however would require knowledge of H in order to construct W. In practice, this is more feasible for a communication system operating in time division duplex (TDD) mode. Thus, for a communication system in frequency division duplex (FDD) mode at least, the UE would need to report the status of its channel with respect to the base station, in order to form H. This would result a significant increase of data to be transmitted between a UE and a base station. With a codebook based approach that quantizes a channel into a finite set, a UE would merely need to recommend an index that best matches its channel. However, since the number of transmit antennas is large for FD-MIMO (Full Dimension MIMO, also known as massive-MIMO or large-scale MIMO) schemes, feedbacks of CSI report could be an arduous task as the size of precoder codebook has to be large in order to properly capture possible channel directions.
Consequently, in light of the aforementioned problems, in a setting such as FD-MIMO for MU-MIMO operations there could be alternative methods by which feedback burdens could be drastically reduced relative to convention schemes.